Psychological Statistics Exam Review Notes

Introduction to Statistics

  • Key Terms:

    • Population vs. Sample

    • Population: Entire group

    • Sample: Subset of the population

    • Parameter vs. Statistic

    • Parameter: Characteristic of a population

    • Statistic: Characteristic of a sample

    • Descriptive vs. Inferential Statistics

    • Descriptive: Summarizes characteristics, e.g., measures of central tendency

    • Inferential: Makes predictions about a population based on a sample

    • Theory vs. Hypothesis

    • Theory: General principle or explanation

    • Hypothesis: Testable prediction derived from a theory

  • Four Scales of Measurement:

    1. Nominal:

    • Characteristics: Label and categorize

    • Example: Majors (art history vs. psychology), Room numbers

    1. Ordinal:

    • Characteristics: Categories organized by rank

    • Example: Rank in class, Clothing sizes (S, M, L, XL)

    1. Interval:

    • Characteristics: Equal intervals between categories; no true zero

    • Example: Temperature, IQ

    1. Ratio:

    • Characteristics: Equal intervals, absolute zero

    • Example: Number of correct answers, Time

Research Methods

  • Correlational vs. Experimental Research:

    • Correlation: Measures the relationship between two variables without manipulation

    • Experimental Research: Manipulates one variable (independent) and measures the effect on another (dependent)

  • Important Distinctions:

    • Correlation does not imply causation

Key Research Terms

  • Independent Variable: The variable manipulated in an experiment

  • Dependent Variable: The variable measured

  • Control Condition: The baseline measurement without the experimental treatment

  • Experimental Condition: The measurement taken with the experimental treatment

  • Notation:

    • Σ (summation), X (data value), N (population size), n (sample size)

    • PEMDAS: Order of operations in arithmetic

  • Data Types:

    • Data: Raw facts and figures

    • Data set: Collection of data points

    • Parameter and Statistic: Population and sample metrics

    • Descriptive vs. Inferential Statistics: Defined earlier

    • Sampling Error: Difference between sample statistic and population parameter

    • Theory vs. Hypothesis: Defined earlier

Frequency Distributions

  • Definition: Organizes data into a table or graph as a type of descriptive statistic

  • Frequency Distribution Table: Shows the frequency (count) of scores

  • Calculations:

    • Number of scores

    • Sum of scores

    • Proportions and percentages

  • Percentiles: Percentage of scores at or below a given value

  • Graphing Frequency Distributions: Use of histograms

Central Tendency

  • Definition: Determines a typical or representative value of the dataset

  • Measures of Central Tendency:

    1. Mean:

    • Population mean: ar{ ext{μ}} = rac{ ext{ΣX}}{N}

    • Sample mean: ar{ ext{M}} = rac{ ext{ΣX}}{n}

    • Interpreted as balance point of data distribution

    • Characteristics: Changes if distribution changes (adding/removing scores affects mean)

    1. Median:

    • The middle value when ordered

    • Divides dataset into two equal groups

    1. Mode:

    • The most frequent score in the distribution

    • Can have bimodal or multimodal distributions

Graphical Representation of Data

  • Goal of Graphs: Show data clearly, make large datasets understandable, aid interpretation

  • Potential Issues with Poor Graphs: Can distort understanding of data

  • Types of Graphs:

    • Pie charts

    • Histograms

    • Bar graphs

    • Line graphs

    • Scatter plots

Variability

  • Definition: Measures the spread of scores

  • Four Measures of Variability:

    1. Range:

    • X{ ext{max}} - X{ ext{min}}

    • Limitations include being imprecise due to extreme values

    1. Interquartile Range (IQR):

    • ext{IQR} = Q3 - Q1

    • Measures distance between the 25th and 75th percentiles

    1. Standard Deviation:

    • Measures average distance from the mean

    • Deviations are calculated as: X - ext{μ} or X - ext{M}

    • Variance is the mean of squared deviations

    1. Variance Calculation

    • Population variance formula is: ext{Variance} = rac{ ext{SS}}{N}

    • Sample variance formula is: ext{Variance} = rac{ ext{SS}}{n-1}

Z-Scores

  • Definition: Describes the position of a score in relation to the mean

  • Formula for Z-Score:

    • From raw score to z-score: z = rac{X - ext{μ}}{ ext{σ}}

    • From z-score to raw score: X = ext{μ} + z ext{σ}

  • Sample Notation: Mean as M and standard deviation as s

  • Z-score Distribution: Transformation keeps shape; mean = 0, standard deviation = 1

  • Purpose of Z-Scores: Enables comparisons across different distributions

Review Questions

  • Ensure to bring your calculator and a pen to the upcoming class and review worksheet